bkm7: Optimal Risky Portfolios

Question 1

Portfolio Risk & equation for equally weighted assets

Answer 1

total variance of portfolio

Question 2

Systemic risk portion of portfolio risk

Answer 2

Covariance because this equation will approach this as n goes to ∞

Question 3

Efficient diversification

Answer 3

lowest risk level for a given return

Question 4

expected return and variance of return for 2 risky assets

Answer 4

Question 5

if correlation is less than 1

Answer 5

portfolio can be constructed that has lower variance than portfolio with single asset

Question 6

Minimum variance portfolio

Answer 6

portfolio with lowest variance that can be constructed from assets with a certain level of correlation, this is different than optimal portfolio

Question 7

minimum variance portfolio will consist of both D&E if […]

& min variance portfolio will consist of exclusively of D when

Answer 7

1. ρ<σ_D/σ_E ​
2. if 1 is not true, will consist of D (lower variance asset) because no benefit to diversification, invest all in lower variance

Question 8

Portfolio opportunity set

Answer 8

plots return as function of std deviation for 2 risky assets for a given correlation

each curve in below graph for given correlation (plot of expected return vs std dev of portfolio that depends on w and correlation)

Question 9

min var portfolio is not

Answer 9

optimal portfolio

CAL(A)=consisting of risk free and min variance portfolio A

can construct CAL(B) with risk free and alternate portfolio B with steeper slope aka higher Sharpe ratio that also intersects portfolio opportunity set

Question 10

Optimal risky portfolio

Answer 10

available portfolio that has highest Sharpe-> portfolio where CAL is tangential to portfolio opportunity set

contains only risky assets which is in contrast to optimal complete portfolio

Question 11

Tangency portfolio

Answer 11

portfolio with CAL tangential to portfolio opportunity set

Question 12

w_D formula for tangency portfolio

Answer 12

Question 13

once optimal risky portfolio weights have been calculated, optimal complete portfolio can be constructed

Answer 13

depends on level of risk aversion

Calculate y, then proportions in D, E, and risk free

Question 14

Minimum-Variance Frontier

Answer 14

portfolios that have lowest variance of each level of expected return

Question 15

Global Min-Var Portfolio:

Answer 15

single portfolio with lowest variance

-investor should invest along frontier and no reason investor should select portfolio below global because top ½ have same risk with higher return

Question 16

Efficient Frontier:

Answer 16

top ½ of min-var frontier

Question 17

Optimal complete portfolio

expected return and variance of return

Answer 17

consists of a risk-free asset and an optimal risky asset portfolio

Question 18

Separation principle:

Answer 18

2 steps in portfolio selection = selection of optimal risky portfolio and allocation between risk free vs risky assets and this will depend on level of risk aversion

-in reality optimal risky can vary between clients due to their unique portfolio constraints -> efficient frontier subject to constraints will have Sharpe ratio that is inferior

Question 19

Risk pooling:

Answer 19

merging several uncorrelated projects together -> selling many uncorrelated insurance policies

• authors argue risk pooling alone actually increases total exposure to risk
• as investor increases risk pooling, both Sharpe and std deviation will increase by n^0.5
• insurer will need to hold more capital to protect against greater risk

Question 20

Risk sharing:

Answer 20

sharing fixed amount of risk among several investors

• higher Sharpe ratio achieved from risk pooling without having to increasing exposure to risk
• can reduce risk by selling shares of insurer to investors -> Sharpe ratio will rise as number of policies increase but risk to each shareholder falls

Question 21

Investment for Long Run

Answer 21

• people believe that extending investments across time will reduce risk
• can think of extending investment horizon to be same as adding additional risky asset to pool
• extending the time horizon increases the Sharpe ratio but std dev will be higher